Circular References - Simultaneous Equations

[Guest]

I am trying to use Excel 2000 to calculate the radius of the arc created by
taking a slice off the top of the circle.

I know the height of the slice (y1) and the length of the base of the slice.

If the point at which the base intersects the circle is designated 'A', the
Radius at point A is calculated as: R² = x² +y² where
x=0.5 x base length (8.0units) and
y=(Radius minus the height of the slice) = (R-2.4units)

R² therefore equals (8² + (R-2.4)² ) - Answer is 14.5333 by simultaneous
equations.

Trouble is, to calculate this in Excel results in a circular referece for
the value of 'R'.

Can anyone assist me to create a formula as I need to look at 100's of other
values?

Thanks in anticipation

 

[Guest]

Damn!! When I entered my question, it was all so neat - except all my little
'squared' (2) signs have all appeared as "&#178" - which is a lot harder to
understand. I hope someone will take the trouble to 'translate' my question.

Andrew

 

[Jerry W. Lewis]

A little algebra give the solution to R^2 = x^2 + (R-h)^2 as
R = (x^2 + h^2)/h/2
If you had a problem that was algebraically intractable, you could use
Solver to numerically approximate the answer.

Jerry

 

[Guest]

Jerry,
If you get to read this, -Thanks for your help! Obviously I need to work
the equation much further than I had been, before Excel can deal with it!

Appreciate your time.
Andrew

 

[Jerry W. Lewis]

You're welcome.

Jerry

 

[Willy Sinclair]

I am trying to use Excel 2000 to calculate the radius of the arc created by
taking a slice off the top of the circle.

I know the height of the slice (y1) and the length of the base of the slice.

If the point at which the base intersects the circle is designated 'A', the
Radius at point A is calculated as: R² = x² +y² where
x=0.5 x base length (8.0units) and
y=(Radius minus the height of the slice) = (R-2.4units)

R² therefore equals (8² + (R-2.4)² ) - Answer is 14.5333 by simultaneous
equations.

Trouble is, to calculate this in Excel results in a circular referece for
the value of 'R'.

Can anyone assist me to create a formula as I need to look at 100's of other
values?

Thanks in anticipation

 

[David Biddulph]

It's a question of algebra, not of Excel.

If R² therefore equals (8² + (R-2.4)² ), expand the terms and cancel the R²
terms.
0=8² + 2.4² -2*R*2.4
Hence R = (8² + 2.4² )/(2*2.4) which gives you your 14.5333 ; no
simultaneous equations.

 

[Willy Sinclair]

I am trying to use Excel 2000 to calculate the radius of the arc created by
taking a slice off the top of the circle.

I know the height of the slice (y1) and the length of the base of the slice.

If the point at which the base intersects the circle is designated 'A', the
Radius at point A is calculated as: R² = x² +y² where
x=0.5 x base length (8.0units) and
y=(Radius minus the height of the slice) = (R-2.4units)

R² therefore equals (8² + (R-2.4)² ) - Answer is 14.5333 by simultaneous
equations.

Trouble is, to calculate this in Excel results in a circular referece for
the value of 'R'.

Can anyone assist me to create a formula as I need to look at 100's of other
values?

Thanks in anticipation

It's a long time since your question but anyway...

A diameter perpendicularly through the base of a sector is related as follows
half the base length squared = the sector height (y1) times (circle diameter
- y1)
You should be able to calculate the diameter and therebt the radius from this

 

[Pete_UK]

It's a long time since your question but anyway...

I doubt if he is still monitoring the post after 3 years !!

Pete